results for au:Shah_A in:gr-qc

- Feb 15 2018 gr-qc arXiv:1802.05241v1We report on a new all-sky search for periodic gravitational waves in the frequency band 475-2000 Hz and with a frequency time derivative in the range of [-1.0e-8, +1e-9] Hz/s. Potential signals could be produced by a nearby spinning and slightly non-axisymmetric isolated neutron star in our galaxy. This search uses the data from Advanced LIGO's first observational run O1. No gravitational wave signals were observed, and upper limits were placed on their strengths. For completeness, results from the separately published low frequency search 20-475 Hz are included as well. Our lowest upper limit on worst-case (linearly polarized) strain amplitude h_0 is 4e-25 near 170 Hz, while at the high end of our frequency range we achieve a worst-case upper limit of 1.3e-24. For a circularly polarized source (most favorable orientation), the smallest upper limit obtained is ~1.5e-25.
- Dec 05 2017 gr-qc astro-ph.CO arXiv:1712.01168v1Cosmic strings are topological defects which can be formed in GUT-scale phase transitions in the early universe. They are also predicted to form in the context of string theory. The main mechanism for a network of Nambu-Goto cosmic strings to lose energy is through the production of loops and the subsequent emission of gravitational waves, thus offering an experimental signature for the existence of cosmic strings. Here we report on the analysis conducted to specifically search for gravitational-wave bursts from cosmic string loops in the data of Advanced LIGO 2015-2016 observing run (O1). No evidence of such signals was found in the data, and as a result we set upper limits on the cosmic string parameters for three recent loop distribution models. In this paper, we initially derive constraints on the string tension $G\mu$ and the intercommutation probability, using not only the burst analysis performed on the O1 data set, but also results from the previously published LIGO stochastic O1 analysis, pulsar timing arrays, cosmic microwave background and Big-Bang nucleosynthesis experiments. We show that these data sets are complementary in that they probe gravitational waves produced by cosmic string loops during very different epochs. Finally, we show that the data sets exclude large parts of the parameter space of the three loop distribution models we consider.
- Nov 16 2017 astro-ph.HE gr-qc arXiv:1711.05578v1On June 8, 2017 at 02:01:16.49 UTC, a gravitational-wave signal from the merger of two stellar-mass black holes was observed by the two Advanced LIGO detectors with a network signal-to-noise ratio of 13. This system is the lightest black hole binary so far observed, with component masses $12^{+7}_{-2}\,M_\odot$ and $7^{+2}_{-2}\,M_\odot$ (90% credible intervals). These lie in the range of measured black hole masses in low-mass X-ray binaries, thus allowing us to compare black holes detected through gravitational waves with electromagnetic observations. The source's luminosity distance is $340^{+140}_{-140}$ Mpc, corresponding to redshift $0.07^{+0.03}_{-0.03}$. We verify that the signal waveform is consistent with the predictions of general relativity.
- Oct 26 2017 astro-ph.HE gr-qc arXiv:1710.09320v1The first observation of a binary neutron star coalescence by the Advanced LIGO and Advanced Virgo gravitational-wave detectors offers an unprecedented opportunity to study matter under the most extreme conditions. After such a merger, a compact remnant is left over whose nature depends primarily on the masses of the inspiralling objects and on the equation of state of nuclear matter. This could be either a black hole or a neutron star (NS), with the latter being either long-lived or too massive for stability implying delayed collapse to a black hole. Here, we present a search for gravitational waves from the remnant of the binary neutron star merger GW170817 using data from Advanced LIGO and Advanced Virgo. We search for short ($\lesssim1$ s) and intermediate-duration ($\lesssim 500$ s) signals, which includes gravitational-wave emission from a hypermassive NS or supramassive NS, respectively. We find no signal from the post-merger remnant. Our derived strain upper limits are more than an order of magnitude larger than those predicted by most models. For short signals, our best upper limit on the root-sum-square of the gravitational-wave strain emitted from 1--4 kHz is $h_{\rm rss}^{50\%}=2.1\times 10^{-22}$ Hz$^{-1/2}$ at 50% detection efficiency. For intermediate-duration signals, our best upper limit at 50% detection efficiency is $h_{\rm rss}^{50\%}=8.4\times 10^{-22}$ Hz$^{-1/2}$ for a millisecond magnetar model, and $h_{\rm rss}^{50\%}=5.9\times 10^{-22}$ Hz$^{-1/2}$ for a bar-mode model. These results indicate that post-merger emission from a similar event may be detectable when advanced detectors reach design sensitivity or with next-generation detectors.
- Oct 17 2017 gr-qc arXiv:1710.05837v1The LIGO Scientific and Virgo Collaborations have announced the first detection of gravitational waves from the coalescence of two neutron stars. The merger rate of binary neutron stars estimated from this event suggests that distant, unresolvable binary neutron stars create a significant astrophysical stochastic gravitational-wave background. The binary neutron star background will add to the background from binary black holes, increasing the amplitude of the total astrophysical background relative to previous expectations. In the Advanced LIGO-Virgo frequency band most sensitive to stochastic backgrounds (near 25 Hz), we predict a total astrophysical background with amplitude $\Omega_{\rm GW} (f=25 \text{Hz}) = 1.8_{-1.3}^{+2.7} \times 10^{-9}$ with $90\%$ confidence, compared with $\Omega_{\rm GW} (f=25 \text{Hz}) = 1.1_{-0.7}^{+1.2} \times 10^{-9}$ from binary black holes alone. Assuming the most probable rate for compact binary mergers, we find that the total background may be detectable with a signal-to-noise-ratio of 3 after 40 months of total observation time, based on the expected timeline for Advanced LIGO and Virgo to reach their design sensitivity.
- Oct 09 2017 gr-qc astro-ph.HE arXiv:1710.02327v2Spinning neutron stars asymmetric with respect to their rotation axis are potential sources of continuous gravitational waves for ground-based interferometric detectors. In the case of known pulsars a fully coherent search, based on matched filtering, which uses the position and rotational parameters obtained from electromagnetic observations, can be carried out. Matched filtering maximizes the signal-to-noise (SNR) ratio, but a large sensitivity loss is expected in case of even a very small mismatch between the assumed and the true signal parameters. For this reason, \it narrow-band analyses methods have been developed, allowing a fully coherent search for gravitational waves from known pulsars over a fraction of a hertz and several spin-down values. In this paper we describe a narrow-band search of eleven pulsars using data from Advanced LIGO's first observing run. Although we have found several initial outliers, further studies show no significant evidence for the presence of a gravitational wave signal. Finally, we have placed upper limits on the signal strain amplitude lower than the spin-down limit for 5 of the 11 targets over the bands searched: in the case of J1813-1749 the spin-down limit has been beaten for the first time. For an additional 3 targets, the median upper limit across the search bands is below the spin-down limit. This is the most sensitive narrow-band search for continuous gravitational waves carried out so far.
- Sep 28 2017 gr-qc arXiv:1709.09203v1We present results from the first directed search for nontensorial gravitational waves. While general relativity allows for tensorial (plus and cross) modes only, a generic metric theory may, in principle, predict waves with up to six different polarizations. This analysis is sensitive to continuous signals of scalar, vector or tensor polarizations, and does not rely on any specific theory of gravity. After searching data from the first observation run of the advanced LIGO detectors for signals at twice the rotational frequency of 200 known pulsars, we find no evidence of gravitational waves of any polarization. We report the first upper limits for scalar and vector strains, finding values comparable in magnitude to previously-published limits for tensor strain. Our results may be translated into constraints on specific alternative theories of gravity.
- Sep 28 2017 gr-qc astro-ph.HE arXiv:1709.09660v3On August 14, 2017 at 10:30:43 UTC, the Advanced Virgo detector and the two Advanced LIGO detectors coherently observed a transient gravitational-wave signal produced by the coalescence of two stellar mass black holes, with a false-alarm-rate of $\lesssim$ 1 in 27000 years. The signal was observed with a three-detector network matched-filter signal-to-noise ratio of 18. The inferred masses of the initial black holes are $30.5_{-3.0}^{+5.7}$ Msun and $25.3_{-4.2}^{+2.8}$ Msun (at the 90% credible level). The luminosity distance of the source is $540_{-210}^{+130}~\mathrm{Mpc}$, corresponding to a redshift of $z=0.11_{-0.04}^{+0.03}$. A network of three detectors improves the sky localization of the source, reducing the area of the 90% credible region from 1160 deg$^2$ using only the two LIGO detectors to 60 deg$^2$ using all three detectors. For the first time, we can test the nature of gravitational wave polarizations from the antenna response of the LIGO-Virgo network, thus enabling a new class of phenomenological tests of gravity.
- Jul 11 2017 gr-qc astro-ph.IM arXiv:1707.02667v2We report on an all-sky search for periodic gravitational waves in the frequency band 20-475 Hz and with a frequency time derivative in the range of [-1.0, +0.1]e-8 Hz/s. Such a signal could be produced by a nearby spinning and slightly non-axisymmetric isolated neutron star in our galaxy. This search uses the data from Advanced LIGO's first observational run, O1. No periodic gravitational wave signals were observed, and upper limits were placed on their strengths. The lowest upper limits on worst-case (linearly polarized) strain amplitude h0 are 4e-25 near 170 Hz. For a circularly polarized source (most favorable orientation), the smallest upper limits obtained are 1.5e-25. These upper limits refer to all sky locations and the entire range of frequency derivative values. For a population-averaged ensemble of sky locations and stellar orientations, the lowest upper limits obtained for the strain amplitude are 2.5e-25.
- Jul 11 2017 gr-qc arXiv:1707.02669v2We report results of a deep all-sky search for periodic gravitational waves from isolated neutron stars in data from the first Advanced LIGO observing run. This search investigates the low frequency range of Advanced LIGO data, between 20 and 100 Hz, much of which was not explored in initial LIGO. The search was made possible by the computing power provided by the volunteers of the Einstein@Home project. We find no significant signal candidate and set the most stringent upper limits to date on the amplitude of gravitational wave signals from the target population, corresponding to a sensitivity depth of 48.7 [1/$\sqrt{{\textrm{Hz}}}$]. At the frequency of best strain sensitivity, near 100 Hz, we set 90% confidence upper limits of $1.8 \times 10^{-25}$. At the low end of our frequency range, 20 Hz, we achieve upper limits of $3.9 \times 10^{-24}$. At 55 Hz we can exclude sources with ellipticities greater than $10^{-5}$ within 100 pc of Earth with fiducial value of the principal moment of inertia of $10^{38} \textrm{kg m}^2$.
- Jun 13 2017 astro-ph.HE gr-qc arXiv:1706.03119v3We present the results of a semicoherent search for continuous gravitational waves from the low-mass X-ray binary Scorpius X-1, using data from the first Advanced LIGO observing run. The search method uses details of the modelled, parametrized continuous signal to combine coherently data separated by less than a specified coherence time, which can be adjusted to trade off sensitivity against computational cost. A search was conducted over the frequency range from 25 Hz to 2000 Hz, spanning the current observationally-constrained range of the binary orbital parameters. No significant detection candidates were found, and frequency-dependent upper limits were set using a combination of sensitivity estimates and simulated signal injections. The most stringent upper limit was set at 175 Hz, with comparable limits set across the most sensitive frequency range from 100 Hz to 200 Hz. At this frequency, the 95 pct upper limit on signal amplitude h0 is 2.3e-25 marginalized over the unknown inclination angle of the neutron star's spin, and 8.03e-26 assuming the best orientation (which results in circularly polarized gravitational waves). These limits are a factor of 3-4 stronger than those set by other analyses of the same data, and a factor of about 7 stronger than the best upper limits set using initial LIGO data. In the vicinity of 100 Hz, the limits are a factor of between 1.2 and 3.5 above the predictions of the torque balance model, depending on inclination angle, if the most likely inclination angle of 44 degrees is assumed, they are within a factor of 1.7.
- Jun 07 2017 gr-qc astro-ph.HE arXiv:1706.01812v1We describe the observation of GW170104, a gravitational-wave signal produced by the coalescence of a pair of stellar-mass black holes. The signal was measured on January 4, 2017 at 10:11:58.6 UTC by the twin advanced detectors of the Laser Interferometer Gravitational-Wave Observatory during their second observing run, with a network signal-to-noise ratio of 13 and a false alarm rate less than 1 in 70,000 years. The inferred component black hole masses are $31.2^{+8.4}_{-6.0}\,M_\odot$ and $19.4^{+5.3}_{-5.9}\,M_\odot$ (at the 90% credible level). The black hole spins are best constrained through measurement of the effective inspiral spin parameter, a mass-weighted combination of the spin components perpendicular to the orbital plane, $\chi_\mathrm{eff} = -0.12^{+0.21}_{-0.30}.$ This result implies that spin configurations with both component spins positively aligned with the orbital angular momentum are disfavored. The source luminosity distance is $880^{+450}_{-390}~\mathrm{Mpc}$ corresponding to a redshift of $z = 0.18^{+0.08}_{-0.07}$. We constrain the magnitude of modifications to the gravitational-wave dispersion relation and perform null tests of general relativity. Assuming that gravitons are dispersed in vacuum like massive particles, we bound the graviton mass to $m_g \le 7.7 \times 10^{-23}~\mathrm{eV}/c^2$. In all cases, we find that GW170104 is consistent with general relativity.
- Apr 18 2017 gr-qc arXiv:1704.04628v4During their first observational run, the two Advanced LIGO detectors attained an unprecedented sensitivity, resulting in the first direct detections of gravitational-wave signals and GW151226, produced by stellar-mass binary black hole systems. This paper reports on an all-sky search for gravitational waves (GWs) from merging intermediate mass black hole binaries (IMBHBs). The combined results from two independent search techniques were used in this study: the first employs a matched-filter algorithm that uses a bank of filters covering the GW signal parameter space, while the second is a generic search for GW transients (bursts). No GWs from IMBHBs were detected, therefore, we constrain the rate of several classes of IMBHB mergers. The most stringent limit is obtained for black holes of individual mass $100\,M_\odot$, with spins aligned with the binary orbital angular momentum. For such systems, the merger rate is constrained to be less than $0.93~\mathrm{Gpc^{-3}\,yr}^{-1}$ in comoving units at the $90\%$ confidence level, an improvement of nearly 2 orders of magnitude over previous upper limits.
- Apr 13 2017 gr-qc arXiv:1704.03719v3Results are presented from a semi-coherent search for continuous gravitational waves from the brightest low-mass X-ray binary, Scorpius X-1, using data collected during the first Advanced LIGO observing run (O1). The search combines a frequency domain matched filter (Bessel-weighted $\mathcal{F}$-statistic) with a hidden Markov model to track wandering of the neutron star spin frequency. No evidence of gravitational waves is found in the frequency range 60-650 Hz. Frequentist 95% confidence strain upper limits, $h_0^{95\%} = 4.0\times10^{-25}$, $8.3\times10^{-25}$, and $3.0\times10^{-25}$ for electromagnetically restricted source orientation, unknown polarization, and circular polarization, respectively, are reported at 106 Hz. They are $\leq 10$ times higher than the theoretical torque-balance limit at 106 Hz.
- Nov 28 2016 gr-qc arXiv:1611.08291v1We study perturbations of Schwarzschild spacetime in a coordinate-free, covariant form. The GHP formulation, having the advantage of not only being covariant but also tetrad-rotation invariant, is used to write down the previously known odd- and even-parity gauge-invariants and the equations they satisfy. Additionally, in the even-parity sector, a new invariant and the second order hyperbolic equation it satisfies are presented. Chandrasekhar's work on transformations of solutions for perturbation equations on Schwarzschild spacetime is translated into the GHP form, i.e., solutions for the equations of the even- and odd-parity invariants are written in terms of one another, and the extreme Weyl scalars; and solutions for the equations of these latter invariants are also written in terms of one another. Recently, further gauge invariants previously used by Steven Detweiler have been described. His method is translated into GHP form and his basic invariants are presented here. We also show how these invariants can be written in terms of curvature invariants.
- Jun 02 2016 gr-qc arXiv:1606.00207v2We introduce a new, resummed, analytical form of the post-Newtonian (PN), factorized, multipolar amplitude corrections $f_{\ell m}$ of the effective-one-body (EOB) gravitational waveform of spinning, nonprecessing, circularized, coalescing black hole binaries (BBHs). This stems from the following two-step paradigm: (i) the factorization of the orbital (spin-independent) terms in $f_{\ell m}$; (ii) the resummation of the residual spin (or orbital) factors. We find that resumming the residual spin factor by taking its inverse resummed (iResum) is an efficient way to obtain amplitudes that are more accurate in the strong-field, fast-velocity regime. The performance of the method is illustrated on the $\ell=2$ and $m=(1,2)$ waveform multipoles, both for a test-mass orbiting around a Kerr black hole and for comparable-mass BBHs. In the first case, the iResum $f_{\ell m}$'s are much closer to the corresponding "exact" functions (obtained solving numerically the Teukolsky equation) up to the light-ring, than the nonresummed ones, especially when the black-hole spin is nearly extremal. The iResum paradigm is also more efficient than including higher post-Newtonian terms (up to 20PN order): the resummed 5PN information yields per se a rather good numerical/analytical agreement at the last-stable-orbit, and a well-controlled behavior up to the light-ring. For comparable mass binaries (including the highest PN-order information available, 3.5PN), comparing EOB with Numerical Relativity (NR) data shows that the analytical/numerical fractional disagreement at merger, without NR-calibration of the EOB waveform, is generically reduced by iResum, from a $40\%$ of the usual approach to just a few percents. This suggests that EOBNR waveform models for coalescing BBHs may be improved using iResum amplitudes.
- Aug 18 2015 gr-qc arXiv:1508.04031v1It is known that a near-extremal Kerr black hole can be spun up beyond its extremal limit by capturing a test particle. Here we show that overspinning is always averted once back-reaction from the particle's own gravity is properly taken into account. We focus on nonspinning, uncharged, massive particles thrown in along the equatorial plane, and work in the first-order self-force approximation (i.e., we include all relevant corrections to the particle's acceleration through linear order in the ratio, assumed small, between the particle's energy and the black hole's mass). Our calculation is a numerical implementation of a recent analysis by two of us [Phys.\ Rev.\ D \bf 91, 104024 (2015)], in which a necessary and sufficient "censorship" condition was formulated for the capture scenario, involving certain self-force quantities calculated on the one-parameter family of unstable circular geodesics in the extremal limit. The self-force information accounts both for radiative losses and for the finite-mass correction to the critical value of the impact parameter. Here we obtain the required self-force data, and present strong evidence to suggest that captured particles never drive the black hole beyond its extremal limit. We show, however, that, within our first-order self-force approximation, it is possible to reach the extremal limit with a suitable choice of initial orbital parameters. To rule out such a possibility would require (currently unavailable) information about higher-order self-force corrections.
- Jun 17 2015 gr-qc arXiv:1506.04755v3We present the first numerical calculation of the (local) metric perturbation produced by a small compact object moving on an eccentric equatorial geodesic around a Kerr black hole, accurate to first order in the mass ratio. The procedure starts by first solving the Teukolsky equation to obtain the Weyl scalar $\psi_4$ using semi-analytical methods. The metric perturbation is then reconstructed from $\psi_4$ in an (outgoing) radiation gauge, adding the appropriate non-radiative contributions arising from the shifts in mass and angular momentum of the spacetime. As a demonstration we calculate the generalized redshift $U$ as a function of the orbital frequencies $\Omega_r$ and $\Omega_\phi$ to linear order in the mass ratio, a gauge invariant measure of the conservative corrections to the orbit due to self-interactions. In Schwarzschild, the results surpass the existing result in the literature in accuracy, and we find new estimates for some of the unknown 4PN and 5PN terms in the post-Newtonian expansion of $U$. In Kerr, we provide completely novel values of $U$ for eccentric equatorial orbits. Calculation of the full self-force will appear in a forthcoming paper.
- In this paper we generalize the spin-raising and lowering operators of spin-weighted spherical harmonics to linear-in-$\gamma$ spin-weighted spheroidal harmonics where $\gamma$ is an additional parameter present in the second order ordinary differential equation governing these harmonics. One can then generalize these operators to higher powers in $\gamma$. Constructing these operators required calculating the $\ell$-, $s$- and $m$-raising and lowering operators (and various combinations of them) of spin-weighted spherical harmonics which have been calculated and shown explicitly in this paper.
- Mar 10 2015 gr-qc arXiv:1503.02638v2It is now possible to compute linear in mass-ratio terms in the post-Newtonian (PN) expansion for compact binaries to very high orders using black hole perturbation theory applied to various invariants. For instance, a computation of the redshift invariant of a point particle in a circular orbit about a black hole in linear perturbation theory gives the linear-in-mass-ratio portion of the binding energy of a circular binary with arbitrary mass ratio. This binding energy, in turn, encodes the system's conservative dynamics. We give a method for extracting the analytic forms of these PN coefficients from high-accuracy numerical data using experimental mathematics techniques, notably an integer relation algorithm. Such methods should be particularly important when the calculations progress to the considerably more difficult case of perturbations of the Kerr metric. As an example, we apply this method to the redshift invariant in Schwarzschild. Here we obtain analytic coefficients to 12.5PN, and higher-order terms in mixed analytic-numerical form to 21.5PN, including analytic forms for the complete 13.5PN coefficient, and all the logarithmic terms at 13PN. At these high orders, an individual coefficient can have over 30 terms, including a wide variety of transcendental numbers, when written out in full. We are still able to obtain analytic forms for such coefficients from the numerical data through a careful study of the structure of the expansion. The structure we find also allows us to predict certain "leading logarithm"-type contributions to all orders. The additional terms in the expansion we obtain improve the accuracy of the PN series for the redshift observable, even in the very strong-field regime inside the innermost stable circular orbit, particularly when combined with exponential resummation.
- Mar 10 2015 gr-qc arXiv:1503.02414v2Using black hole perturbation theory and arbitrary-precision computer algebra, we obtain the post-Newtonian (pN) expansions of the linear-in-mass-ratio corrections to the spin-precession angle and tidal invariants for a particle in circular orbit around a Schwarzschild black hole. We extract coefficients up to 20pN order from numerical results that are calculated with an accuracy greater than 1 part in $10^{500}$. These results can be used to calibrate parameters in effective-one-body models of compact binaries, specifically the spin-orbit part of the effective Hamiltonian and the dynamically significant tidal part of the main radial potential of the effective metric. Our calculations are performed in a radiation gauge, which is known to be singular away from the particle. To overcome this irregularity, we define suitable Detweiler-Whiting singular and regular fields in this gauge, and we devise a rigorous mode-sum regularization method to compute the invariants constructed from the regular field.
- Oct 14 2014 gr-qc arXiv:1410.2998v2We present a first numerical implementation of a new scheme by Pound et al. that enables the calculation of the gravitational self-force in Kerr spacetime from a reconstructed metric-perturbation in a radiation gauge. The numerical task of the metric reconstruction essentially reduces to solving the fully separable Teukolsky equation, rather than having to tackle the linearized Einstein's equations themselves. The method offers significant computational saving compared to existing methods in the Lorenz gauge, and we expect it to become a main workhorse for precision self-force calculations in the future. Here we implement the method for circular orbits on a Schwarzschild background, in order to illustrate its efficacy and accuracy. We use two independent methods for solving the Teukolsky equation, one based on a direct numerical integration, and the other on the analytical approach of Mano, Suzuki, and Takasugi. The relative accuracy of the output self-force is at least $10^{-7}$ using the first method, and at least $10^{-9}$ using the second; the two methods agree to within the error bars of the first. We comment on the relation to a related approach by Shah et al., and discuss foreseeable applications to more generic orbits in Kerr spacetime.
- Apr 25 2014 gr-qc astro-ph.HE arXiv:1404.6133v2For a self-gravitating particle of mass \mu in orbit around a Kerr black hole of mass M >> \mu, we compute the O(\mu/M) shift in the frequency of the innermost stable circular equatorial orbit (ISCEO) due to the conservative piece of the gravitational self-force acting on the particle. Our treatment is based on a Hamiltonian formulation of the dynamics in terms of geodesic motion in a certain locally-defined effective smooth spacetime. We recover the same result using the so-called first law of binary black-hole mechanics. We give numerical results for the ISCEO frequency shift as a function of the black hole's spin amplitude, and compare with predictions based on the post-Newtonian approximation and the effective one-body model. Our results provide an accurate strong-field benchmark for spin effects in the general relativistic two-body problem.
- Mar 12 2014 gr-qc arXiv:1403.2697v2In this article we present the post-Newtonian (pN) coefficients of the energy flux (and angular momentum flux) at infinity and event horizon for a particle in circular, equatorial orbits about a Kerr black hole (of mass $M$ and spin-parameter $a$) up to 20-pN order. When a pN term is not a polynomial in $a/M$ and includes irrational functions (like polygamma functions), it is written as a power series of $a/M$. This is achieved by calculating the fluxes numerically with an accuracy greater than 1 part in $10^{600}$. Such high accuracy allows us to extract analytical values of pN coefficients that are linear combinations of transcendentals like the Euler constant, logarithms of prime numbers and powers of $\pi$. We also present the 22-pN expansion (spin-independent pN expansion) of the ingoing energy flux at the event horizon for a particle in circular orbit about a Schwarzschild black hole.
- Dec 09 2013 gr-qc arXiv:1312.1952v2We present a novel analytic extraction of high-order post-Newtonian (pN) parameters that govern quasi-circular binary systems. Coefficients in the pN expansion of the energy of a binary system can be found from corresponding coefficients in an extreme-mass-ratio inspiral (EMRI) computation of the change $\Delta U$ in the redshift factor of a circular orbit at fixed angular velocity. Remarkably, by computing this essentially gauge-invariant quantity to accuracy greater than one part in $10^{225}$, and by assuming that a subset of pN coefficients are rational numbers or products of $\pi$ and a rational, we obtain the exact analytic coefficients. We find the previously unexpected result that the post-Newtonian expansion of $\Delta U$ (and of the change $\Delta\Omega$ in the angular velocity at fixed redshift factor) have conservative terms at half-integral pN order beginning with a 5.5 pN term. This implies the existence of a corresponding 5.5 pN term in the expansion of the energy of a binary system. Coefficients in the pN series that do not belong to the subset just described are obtained to accuracy better than 1 part in $10^{265-23n}$ at $n$th pN order. We work in a radiation gauge, finding the radiative part of the metric perturbation from the gauge-invariant Weyl scalar $\psi_0$ via a Hertz potential. We use mode-sum renormalization, and find high-order renormalization coefficients by matching a series in $L=\ell+1/2$ to the large-$L$ behavior of the expression for $\Delta U$. The non-radiative parts of the perturbed metric associated with changes in mass and angular momentum are calculated in the Schwarzschild gauge.
- Mar 28 2013 gr-qc arXiv:1303.6829v2The orbital motion is derived for a non-spinning test-mass in the relativistic, gravitational field of a rotationally deformed body not restricted to the equatorial plane or spherical orbit. The gravitational field of the central body is represented by the Kerr metric, expanded to second post-Newtonian order including the linear and quadratic spin terms. The orbital period, the intrinsic periastron advance, and the precession of the orbital plane are derived with the aid of novel canonical variables and action-based methods.
- Jul 25 2012 gr-qc arXiv:1207.5595v2This is the first of two papers on computing the self-force in a radiation gauge for a particle moving in circular, equatorial orbit about a Kerr black hole. In the EMRI (extreme-mass-ratio inspiral) framework, with mode-sum renormalization, we compute the renormalized value of the quantity $h_{\alpha\beta}u^\alpha u^\beta$, gauge-invariant under gauge transformations generated by a helically symmetric gauge vector; and we find the related order $\frak{m}$ correction to the particle's angular velocity at fixed renormalized redshift (and to its redshift at fixed angular velocity). The radiative part of the perturbed metric is constructed from the Hertz potential which is extracted from the Weyl scalar by an algebraic inversion\citesf2. We then write the spin-weighted spheroidal harmonics as a sum over spin-weighted spherical harmonics and use mode-sum renormalization to find the renormalization coefficients by matching a series in $L=\ell+1/2$ to the large-$L$ behavior of the expression for $H := \frac12 h_{\alpha\beta}u^\alpha u^\beta $. The non-radiative parts of the perturbed metric associated with changes in mass and angular momentum are calculated in the Kerr gauge.
- Sep 27 2010 gr-qc arXiv:1009.4876v4This is the second of two companion papers on computing the self-force in a radiation gauge; more precisely, the method uses a radiation gauge for the radiative part of the metric perturbation, together with an arbitrarily chosen gauge for the parts of the perturbation associated with changes in black-hole mass and spin and with a shift in the center of mass. We compute the conservative part of the self-force for a particle in circular orbit around a Schwarzschild black hole. The gauge vector relating our radiation gauge to a Lorenz gauge is helically symmetric, implying that the quantity h_\alpha\beta u^\alpha u^\beta (= h_uu) must have the same value for our radiation gauge as for a Lorenz gauge; and we confirm this numerically to one part in 10^13. As outlined in the first paper, the perturbed metric is constructed from a Hertz potential that is in term obtained algebraically from the the retarded perturbed spin-2 Weyl scalar, \psi_0 . We use a mode-sum renormalization and find the renormalization coefficients by matching a series in L = \ell + 1/2 to the large-L behavior of the expression for the self-force in terms of the retarded field h_\alpha\beta^ret; we similarly find the leading renormalization coefficients of h_uu and the related change in the angular velocity of the particle due to its self-force. We show numerically that the singular part of the self-force has the form f_\alpha ∝< \nabla_\alpha \rho^-1>, the part of \nabla_\alpha \rho^-1 that is axisymmetric about a radial line through the particle. This differs only by a constant from its form for a Lorenz gauge. It is because we do not use a radiation gauge to describe the change in black-hole mass that the singular part of the self-force has no singularity along a radial line through the particle and, at least in this example, is spherically symmetric to subleading order in \rho.
- Apr 15 2010 gr-qc arXiv:1004.2276v4In this, the first of two companion papers, we present a method for finding the gravitational self-force in a modified radiation gauge for a particle moving on a geodesic in a Schwarzschild or Kerr spacetime. An extension of an earlier result by Wald is used to show the spin-weight $\pm 2$ perturbed Weyl scalar ($\psi_0$ or $\psi_4$) determines the metric perturbation outside the particle up to a gauge transformation and an infinitesimal change in mass and angular momentum. A Hertz potential is used to construct the part of the retarded metric perturbation that involves no change in mass or angular momentum from $\psi_0$ in a radiation gauge. The metric perturbation is completed by adding changes in the mass and angular momentum of the background spacetime outside the radial coordinate $r_0$ of the particle in any convenient gauge. The resulting metric perturbation is singular on the trajectory of the particle and discontinuous across the sphere $r=r_0$. A mode-sum method can be used to renormalize the self-force, but the justification given in the published version of this paper \citesf2 referred to work by Sam Gralla \citegralla10 to justify the use of the renormalized self-force, and the radiation gauge we use does not satisfy the regularity conditions required by Gralla. Instead we show that the renormalized self-force, computed either from the retarded field for $r>r_0$ or for $r<r_0$ gives the correct equations of motion in a gauge smoothly related to a Lorenz gauge; and Pound et al. \citepmb13 argue that the average of the self-force obtained in the way described in our paper for $r>r_0$ and for $r<r_0$ gives the correct equation of motion for our gauge (what Pound et al. call the no-string gauge).